Positioning is a fundamental issue in mobile robot applications. It can be achieved in many ways. Among them, triangulation based on angles measured with the help of beacons is a proven technique. Most of ... [more ▼]

Positioning is a fundamental issue in mobile robot applications. It can be achieved in many ways. Among them, triangulation based on angles measured with the help of beacons is a proven technique. Most of the many triangulation algorithms proposed so far have major limitations. For example, some of them need a particular beacon ordering, have blind spots, or only work within the triangle defined by the three beacons. More reliable methods exist; however, they have an increasing complexity or they require to handle certain spatial arrangements separately. In this paper, we present a simple and new three object triangulation algorithm, named ToTal, that natively works in the whole plane, and for any beacon ordering. We also provide a comprehensive comparison between many algorithms, and show that our algorithm is faster and simpler than comparable algorithms. In addition to its inherent efficiency, our algorithm provides a very useful and unique reliability measure, assessable anywhere in the plane, which can be used to identify pathological cases, or as a validation gate in Kalman filters. [less ▲]

Positioning is a fundamental issue in mobile robot applications, and it can be achieved in multiple ways. Among these methods, triangulation based on angle measurements is widely used, robust, accurate ... [more ▼]

Positioning is a fundamental issue in mobile robot applications, and it can be achieved in multiple ways. Among these methods, triangulation based on angle measurements is widely used, robust, accurate, and flexible. This paper presents BeAMS, a new active beacon-based angle measurement system used for mobile robot positioning. BeAMS introduces several major innovations. One innovation is the use of a unique unsynchronized channel with On-Off Keying modulated infrared signals to measure angles and to identify the beacons. We also introduce a new mechanism to measure angles: our system detects a beacon when it enters and leaves an angular window. We show that the estimator resulting from the center of this angular window provides an unbiased estimate of the beacon angle. A theoretical framework for a thorough performance analysis of BeAMS is provided. We establish the upper bound of the variance and validate this bound through experiments and simulations; the overall error measure of BeAMS is lower than 0.24 deg for an acquisition rate of 10 Hz. In conclusion, BeAMS is a low power, flexible, and robust solution for angle measurement, and a reliable component for robot positioning. [less ▲]

The paper considers the feedback stabilization of periodic orbits in a planar juggler. The juggler is "blind," i.e, he has no other sensing capabilities than the detection of impact times. The robustness ... [more ▼]

The paper considers the feedback stabilization of periodic orbits in a planar juggler. The juggler is "blind," i.e, he has no other sensing capabilities than the detection of impact times. The robustness analysis of the proposed control suggests that the arms acceleration at impact is a crucial design parameter even though it plays no role in the stability analysis. Analytical results and convergence proofs are provided for a simplified model of the juggler. The control law is then adapted to a more accurate model and validated in an experimental setup. [less ▲]

The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2-D bounce juggling. It is shown that some periodic orbits that are unstable in the elastic fixed wedge become ... [more ▼]

The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2-D bounce juggling. It is shown that some periodic orbits that are unstable in the elastic fixed wedge become exponentially stable in the nonelastic vibrating wedge. These orbits are linked with certain classical juggling patterns, providing an interesting benchmark for the study of the frequency-locking properties in human rhythmic tasks. Experimental results on sensorless stabilization of juggling patterns are described. [less ▲]